ss4S2: The required sample size for estimating a single variance

In samplesize4surveys: Sample Size Calculations for Complex Surveys

Description

This function returns the minimum sample size required for estimating a single variance subjecto to predefined errors.

Usage

ss4S2(N, K = 0, DEFF = 1, conf = 0.95, cve = 0.05, me = 0.03, plot = FALSE)

Arguments

N	The population size.
K	The population excess kurtosis of the variable in the population.
DEFF	The design effect of the sample design. By default DEFF = 1, which corresponds to a simple random sampling design.
conf	The statistical confidence. By default conf = 0.95. By default conf = 0.95.
cve	The maximun coeficient of variation that can be allowed for the estimation.
me	The maximun margin of error that can be allowed for the estimation.
plot	Optionally plot the errors (cve and margin of error) against the sample size.

Details

Note that the minimun sample size to achieve a particular relative margin of error \varepsilon is defined by:

n = \frac{n_0}{\frac{(N-1)^3}{N^2(N*K+2N+2)}+\frac{n_0}{N}}

Where

n_0=\frac{z^2_{1-\frac{α}{2}}*DEFF}{\varepsilon^2}

Also note that the minimun sample size to achieve a particular coefficient of variation cve is defined by:

n = \frac{N^2(N*K+2N+2)*DEFF}{cve^2*(N-1)^3+N(N*K+2N+2)*DEFF}

Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

e4p

Examples

ss4S2(N = 10000, K = 0, cve = 0.05, me = 0.03)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.03)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.05, DEFF = 2)
ss4S2(N = 10000, K = 1, cve = 0.05, me = 0.03, plot = TRUE)

#############################
# Example with BigLucy data #
#############################

data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
K <- kurtosis(BigLucy$Income)
# The minimum sample size for simple random sampling
ss4S2(N, K, DEFF=1, conf=0.99, cve=0.03, me=0.1, plot=TRUE)
# The minimum sample size for a complex sampling design
ss4S2(N, K, DEFF=3.45, conf=0.99, cve=0.03, me=0.1, plot=TRUE)

Example output

Loading required package: TeachingSampling
Loading required package: timeDate
With the parameters of this function: N = 10000 DEFF =  1 conf = 0.95 .

             The estimated sample size to obtain a maximun coefficient of variation of 5 % is n= 742 .
             The estimated sample size to obtain a maximun relative margin of error of 3 % is n= 4607 . 
 
$n.cve
[1] 742

$n.me
[1] 4607

With the parameters of this function: N = 10000 DEFF =  1 conf = 0.95 .

             The estimated sample size to obtain a maximun coefficient of variation of 5 % is n= 1072 .
             The estimated sample size to obtain a maximun relative margin of error of 3 % is n= 5616 . 
 
$n.cve
[1] 1072

$n.me
[1] 5616

With the parameters of this function: N = 10000 DEFF =  2 conf = 0.95 .

             The estimated sample size to obtain a maximun coefficient of variation of 5 % is n= 1937 .
             The estimated sample size to obtain a maximun relative margin of error of 5 % is n= 4798 . 
 
$n.cve
[1] 1937

$n.me
[1] 4798

With the parameters of this function: N = 10000 DEFF =  1 conf = 0.95 .

             The estimated sample size to obtain a maximun coefficient of variation of 5 % is n= 1072 .
             The estimated sample size to obtain a maximun relative margin of error of 3 % is n= 5616 . 
 
$n.cve
[1] 1072

$n.me
[1] 5616

With the parameters of this function: N = 85296 DEFF =  1 conf = 0.99 .

             The estimated sample size to obtain a maximun coefficient of variation of 3 % is n= 5997 .
             The estimated sample size to obtain a maximun relative margin of error of 10 % is n= 3686 . 
 
$n.cve
[1] 5997
attr(,"method")
[1] "excess"

$n.me
[1] 3686
attr(,"method")
[1] "excess"

With the parameters of this function: N = 85296 DEFF =  3.45 conf = 0.99 .

             The estimated sample size to obtain a maximun coefficient of variation of 3 % is n= 17650 .
             The estimated sample size to obtain a maximun relative margin of error of 10 % is n= 11498 . 
 
$n.cve
[1] 17650
attr(,"method")
[1] "excess"

$n.me
[1] 11498
attr(,"method")
[1] "excess"

samplesize4surveys documentation built on Jan. 18, 2020, 1:11 a.m.